There appears to be no discernible pattern for these numbers, other than them increasing in arbitrary multiples of 6.
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289 because each consecutive prime number is squared.
25 is the next number that appears in that sequence.
The first thing to notice is that all the numbers in the sequence are square numbers. 25=5x5 36=6x6 49=7x7 64=8x8 81=9x9 So the next three numbers to be squared are 10, 11 and 12. 10x10=100 11x11=121 12x12=144 Thus, the next three numbers in the sequence are 100, 121, 144 The equation for the sequence is (n+4)2
Each is half of the previous number, so 6.25 will be next.
This is a sequence of perfect squares. 12=1, 22=4, 32=9, 42=16, 52=25. The next number is 62=36.